Recently, we have introduced two graph-decomposition theorems based on a new graph product [1]}, motivated by applications in the context of synchronising periodic real-time processes, in particular in the field of robotics.
More on the background, definitions, and applications can be found in two conference contributions [2]}, [3]}, two journal papers [1]}, [5]} and the thesis of the author [6]}.
In this contribution, we relax some of the requirements of these two graph-decomposition theorems.
Also, we repeat some of the background, definitions, and theorems here for convenience.
